Digital filter circuit, digital filter processing method and digital filter processing program storage medium

ABSTRACT

Reduction of a circuit size and power consumption for performing digital filtering processing in a frequency domain is realized. The digital filter circuit includes: a complex conjugate generation unit for generating a second complex number signal including conjugate complex numbers of all complex numbers included in a first complex number signal of the frequency domain generated by converting a complex number signal of a time domain by Fourier transform; a filter coefficient generation unit for generating a first and a second frequency domain filter coefficient of a complex number from a first, a second and a third input filter coefficient of a complex number having been inputted; a first filtering unit for performing filtering processing to the first complex number signal by the first frequency domain filter coefficient, and outputting a third complex number signal; a second filtering unit for performing filtering processing to the second complex number signal by the second frequency domain filter coefficient, and outputting a fourth complex number signal; and a complex conjugate combining unit for combining the third complex number signal and the fourth complex number signal, and generating a fifth complex number signal.

TECHNICAL FIELD

The present invention relates to arithmetic processing in digital signalprocessing, and, more particularly, to a digital filter circuit, adigital filter processing method and a digital filter processing programstorage medium.

BACKGROUND ART

There are a FIR (Finite Impulse Response) filter and an IIR (InfiniteImpulse Response) filter as a digital filter being used widely. FIG. 9is an exemplary configuration of a digital filter circuit 100 using aFIR filter.

The digital filter circuit 100 performs filtering processing in a timedomain to complex number signal x(n)=r(n)+js(n) (j is an imaginary unitand n is an integer). The digital filter circuit 100 includes three FIRfilters 101, 102 and 103.

The FIR filter 101 is a FIR filter of a real number coefficient havingthe number of taps of 5, the FIR filter performing filtering processingby real number operation to real part signal r(n) of a real number thatis the real part of inputted complex number signal x(n). Five filtercoefficients a0-a4 of the FIR filter 101 are real numbers. The FIRfilter 101 outputs a result of filtering processing as real part signalr′(n).

Similarly, the FIR filter 102 is a FIR filter of real number coefficienthaving the number of taps of 5, the FIR filter performing filteringprocessing by real number operation to imaginary part signal s(n) of areal number that is the imaginary part of an inputted complex numbersignal. Five filter coefficients b0-b4 of the FIR filter 102 are realnumbers. The FIR filter 102 outputs a result of filtering processing asimaginary part signal s′(n).

The FIR filter 103 is a FIR filter of a complex number coefficienthaving the number of taps of 5, the FIR filter performing filteringprocessing by complex number operation to complex number signalx′(n)=r′(n)+js′(n) that includes real part signal r′(n) and imaginarypart signal s′(n) to which filtering processing has been performed bythe FIR filters 101 and 102. Five filter coefficients c0-c4 of the FIRfilter 103 are complex numbers. The FIR filter 103 outputs a result offiltering processing as complex number signal x″(n).

In the block diagram of FIG. 9, a complex number signal is expressed bya line thicker than a line which indicates a signal of a real number inorder to distinguish them. Hereinafter, lines which indicate a signalare expressed in a similar manner also in other block diagrams.

In filtering processing by a FIR filter, there is a case where both offiltering processing by real number operation using a filter coefficientof a real number and filtering processing by complex number operationusing a filter coefficient of a complex number are performed as is thecase with the digital filter circuit 100.

Generally, a minimum value of the number of taps of a FIR filter isdetermined by an impulse response length of a filter function desired tobe realized. Therefore, when realizing a complicated filter function,the number of taps of more than several hundred taps may be needed.There is a problem that, in a LSI (Large Scale Integrated circuit) onwhich such a FIR filter with a large number of taps is mounted, thecircuit scale and power consumption of the LSI becomes huge.

To cope with this problem, there is known a technology which performsfiltering processing in a frequency domain (patent document 1, forexample). In filtering processing in the frequency domain, signal dataon the time domain is converted into a signal data on the frequencydomain firstly by fast Fourier transform (FFT: Fast Fourier Transform).Then, after filtering calculation between the signal data and a filtercoefficient has been carried out in the frequency domain, it isreconverted by high-speed inverse Fourier transform (IFFT: Inverse FastFourier Transform) into a signal data on the time domain.

In a case where the number of taps of a FIR filter is large, a circuitscale and electric power consumption required for realization offiltering processing can be reduced by performing filtering processingin the frequency domain. The reason is that convolution operation in thetime domain by a FIR filter can be converted into simple multiplicationin the frequency domain.

Meanwhile, when a signal in the time domain is a complex number signal,the complex number signal is converted by a complex FFT into complexnumber signal data of the frequency domain. In complex FFT conversion,the real part and the imaginary part of a complex number signal in thetime domain are combined, and are converted into complex number signaldata in the frequency domain. That is, both of the real part and theimaginary part of a complex number signal in the time domain are usedfor calculation of each of the real part and the imaginary part ofcomplex number signal data in the frequency domain. For this reason,according to the technology of patent document 1, when filteringprocessing is performed independently to each of the real part and theimaginary part of a complex number signal of the time domain, it isnecessary to convert them into signal data of the frequency domain byreal number FFT independently from each other.

In FIG. 10, there is shown an exemplary configuration of a digitalfilter circuit 110 which performs filtering processing in the frequencydomain. The digital filter circuit 110 corresponds to the digital filtercircuit 100 shown in FIG. 9 that performs filtering processing in thetime domain. The digital filter circuit 110 is a digital filter circuitwhich performs filtering processing in the frequency domain to complexnumber signal x(n) (=r(n)+js(n)). The digital filter circuit 110includes three frequency domain filter circuits 111, 112 and 113.

The frequency domain filter 111 converts real part signal r(n) which isthe real part of inputted complex number signal x(n) on the time domainto complex number signal data on the frequency domain by FFT. Then,after performing filtering calculation by complex number operation onthe frequency domain to complex number signal data on the frequencydomain, the frequency domain filter 111 reconverts it into real partsignal data r′(n) on the time domain by IFFT. Although real part signalr(n) is a signal of a real number, signal data after conversion will bea complex number even when Fourier transformation is applied to a signalof a real number. In addition, a filter coefficient is also a complexnumber usually. Therefore, complex number operation is required tofiltering calculation.

Similarly, the frequency domain filter 112 converts imaginary partsignal s(n) of a real number that is the imaginary part of inputtedcomplex number signal x(n) on the time domain into complex number signaldata on the frequency domain by FFT. Then, after performing filteringcalculation by complex number operation on the frequency domain tocomplex number signal data on the frequency domain, the frequency domainfilter 112 reconverts it into imaginary part signal data s′(n) of a realnumber on the time domain by IFFT.

On the other hand, the frequency domain filter 113 converts complexnumber signal x′(n)=r′(n)+js′(n) which includes real part signal r′(n)and imaginary part signal s′(n) into complex number signal data on thefrequency domain by FFT. Then, after performing filtering calculation bycomplex number operation on the frequency domain to complex numbersignal data on the frequency domain, the frequency domain filter 113reconverts it into imaginary part signal data s″(n) of the real numberon the time domain by an IFFT.

A digital filter which handles an input signal as a complex numbersignal is also disclosed in patent document 2.

Further, a technology which performs inverse Fourier transformationafter performing predetermined calculation using a complex number signalgenerated by performing Fourier transformation to an input signal andits complex conjugate value is also disclosed in patent document 3.

CITATION LIST Patent Literature

-   [PTL 1] Japanese Patent Application Laid-Open No. 2011-4264-   [PTL 2] International Publication WO No. 2007/010727-   [PTL 3] Japanese Patent Application Laid-Open Hei No. 2-36385

SUMMARY OF INVENTION Technical Problem

As it is clear from the structure of the digital filter circuit 110shown in FIG. 10, in the technology of patent literature 1, independentfiltering processing by real number operation is performed to each ofthe real part and the imaginary part of a complex number signal toperform filtering processing by complex number operation to the complexnumber signal. Therefore, when the technology of patent document 1 isapplied, FFT and IFFT are needed for filtering processing for each ofthe real part and the imaginary part of a complex number signal byfrequency domain filters. Accordingly, there is a problem that, in a LSIon which the above-mentioned filtering function is mounted, a circuitscale and electric power consumption becomes huge.

Also in the technologies of patent literature 2 and 3, independentfiltering processing is needed for each of the real part and theimaginary part of a complex number signal to perform filteringprocessing by complex number operation to the complex number signal.Accordingly, there is the same problem as patent literature 1 that FFTand IFFT are needed for filtering processing for each of the real partand the imaginary part of a complex number signal by frequency domainfilters.

Object of Invention

The present invention is made for settling the above-mentioned problem,and an object of the present invention is to provide a digital filtercircuit, a digital filter processing method and a digital filterprocessing program storage medium which can achieve reduction of circuitscale and power consumption for performing digital filtering processingin the frequency domain.

Solution to Problem

A digital filter circuit of the present invention comprises: a complexconjugate generation means for generating a second complex number signalincluding respective conjugate complex numbers of all complex numbersincluded in a first complex number signal of a frequency domaingenerated by converting a complex number signal of a time domain byFourier transform; a filter coefficient generation means for generatinga first and a second frequency domain filter coefficient of a complexnumber from a first, a second and a third input filter coefficient of acomplex number having been inputted; a first filtering means forperforming filtering processing to the first complex number signal bythe first frequency domain filter coefficient, and outputting a thirdcomplex number signal; a second filtering means for performing filteringprocessing to the second complex number signal by the second frequencydomain filter coefficient, and outputting a fourth complex numbersignal; and a complex conjugate combining means for combining the thirdcomplex number signal and the fourth complex number signal, andgenerating a fifth complex number signal.

A digital filter processing method of the present invention comprisesthe steps of: generating a second complex number signal includingrespective conjugate complex numbers of all complex numbers included ina first complex number signal of a frequency domain generated byconverting a complex number signal of a time domain by Fouriertransform; generating a first and a second frequency domain filtercoefficient of a complex number from a first, a second and a third inputfilter coefficient of a complex number having been inputted; performingfiltering processing to the first complex number signal by the firstfrequency domain filter coefficient, and outputting a third complexnumber signal; performing filtering processing to the second complexnumber signal by the second frequency domain filter coefficient, andoutputting a fourth complex number signal; and combining the thirdcomplex number signal and the fourth complex number signal, andgenerating a fifth complex number signal.

A digital filter processing program storage medium of the presentinvention stores a program for making a computer provided in anarithmetic device function as: a complex conjugate generation means forgenerating a second complex number signal including respective conjugatecomplex numbers of all complex numbers included in a first complexnumber signal of a frequency domain generated by converting a complexnumber signal of a time domain by Fourier transform; a filtercoefficient generation means for generating a first and a secondfrequency domain filter coefficient of a complex number from a first, asecond and a third input filter coefficient of a complex number havingbeen inputted; a first filtering processing means for performingfiltering processing to the first complex number signal by the firstfrequency domain filter coefficient, and outputting a third complexnumber signal; a second filtering processing means for performingfiltering processing to the second complex number signal by the secondfrequency domain filter coefficient, and outputting a fourth complexnumber signal; and a complex conjugate combining means for combining thethird complex number signal and the fourth complex number signal, andgenerating a fifth complex number signal.

Advantageous Effects of Invention

According to the present invention, reduction of circuit scale and powerconsumption for performing digital filtering processing in a frequencydomain can be achieved.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 A block diagram showing a structure of a digital filter circuitaccording to a first exemplary embodiment of the present invention

FIG. 2 A block diagram showing a structure of a complex conjugategenerating circuit 15 according to the first exemplary embodiment of thepresent invention

FIG. 3 A block diagram showing a structure of a filter circuit 21according to the first exemplary embodiment of the present invention

FIG. 4 A block diagram showing a structure of a filter circuit 22according to the first exemplary embodiment of the present invention.

FIG. 5 A block diagram showing a structure of a complex conjugatecombining circuit 16 according to the first exemplary embodiment of thepresent invention

FIG. 6 A block diagram showing a structure of a filter coefficientgenerating circuit 41 according to the first exemplary embodiment of thepresent invention

FIG. 7 A block diagram of a digital filter circuit having only anindispensable structure of a digital filter circuit according to thefirst exemplary embodiment of the present invention

FIG. 8A A flow chart showing a first example of a processing procedureof a digital filter processing program according to a second exemplaryembodiment of the present invention

FIG. 8B A flow chart showing a second example of a processing procedureof a digital filter processing program according to the second exemplaryembodiment of the present invention

FIG. 9 A block diagram showing an exemplary configuration of a digitalfilter circuit using a FIR filter

FIG. 10 A block diagram showing an exemplary configuration of a digitalfilter circuit which performs a filtering processing in the frequencydomain

DESCRIPTION OF EMBODIMENTS

Next, an exemplary embodiment of the present invention will be describedwith reference to a drawing.

The First Exemplary Embodiment

FIG. 1 is a block diagram showing a structure of a digital filtercircuit 10 according to the first exemplary embodiment of the presentinvention. The digital filter circuit 10 includes a FFT circuit 13, anIFFT circuit 14, the complex conjugate generating circuit 15, thecomplex conjugate combining circuit 16, the filter circuit 21, thefilter circuit 22 and the filter coefficient generating circuit 41.

The following complex number signal in a time domain is inputted to thedigital filter circuit 10.

x(n)=r(n)+js(n)  (1)

The FFT circuit 13 converts inputted complex number signal x(n) into thefollowing complex number signal of a frequency domain by FFT.

X(k)=A(k)+jB(k)  (2)

Here, n is an integer of 0≦n≦N−1 which indicates a signal sample numberon the time domain, N is an integer of 0<N which shows the number ofconversion samples of FFT, and k is an integer of 0≦k≦N−1 which shows afrequency number on the frequency domain.

The FFT circuit 13 generates

X(N−k)=A(N−k)+jB(N−k)  (3)

from X(k), and outputs X(N−k).

Meanwhile, FFT is one method for performing Fourier transform at highspeed. A processing form and a processing speed of Fourier transform arenot essential problems for the present invention. Accordingly, a circuitwhich performs Fourier transform by a method besides FFT is allowed tobe used instead of the FFT circuit 13. This point is also similar aboutIFFT mentioned later.

The complex conjugate generating circuit 15 receives input X(N−k) whichthe FFT circuit 13 outputs about each of frequency number k of 0≦k≦N−1,and generates the following complex conjugate of X(N−k).

X*(N−k)=A(N−k)−jB(N−k)  (4)

The complex conjugate generating circuit 15 outputs inputted complexnumber signal X (k) as a complex number signal 32, and outputs complexnumber signal X*(N−k) which has been generated as a complex numbersignal 33.

Next, about each of frequency number k of 0≦k≦N−1, the filtercoefficient generating circuit 41 generates from inputted complex numbercoefficients V(k), W(k) and H(k) the following two complex numbercoefficients.

C1(k)={V(k)+W(k)}×H(k)  (5)

C2(k)={V(k)−V(k)}×H(k)  (6)

Here, complex number coefficient V(k), W(k) and H(k) are coefficients inthe frequency domain which are given from a higher rank circuit (notshown) of the digital filter circuit 10, and correspond to real numberfilter coefficients when performing filtering processing by real numberoperation in the time domain. Description of details of V(k), W(k) andH(k) will be made later.

The filter coefficient generating circuit 41 outputs generated complexnumber coefficient C1(k) as a complex number signal 45. The filtercoefficient generating circuit 41 generates complex number signalC2(N−k) from complex number signal C2(k) (Formula (6)), and outputsC2(N−k) as a complex number signal 46.

Next, the filter circuit 21 performs complex number filtering processingby complex number multiplication to X(k) (Formula (2)) which the complexconjugate generating circuit 15 outputs to the complex number signal 32,using C1(k) (Formula (5)) which the filter coefficient generatingcircuit 41 outputs to the complex number signal 45. Specifically, abouteach frequency number k of 0≦k≦N−1, the filter circuit 21 calculates acomplex number signal

X′(k)=X(k)×C1(k)  (7)

and outputs it as a complex number signal 34.

Similarly, the filter circuit 22 performs complex number filteringprocessing by complex number multiplication to X*(N−k) (Formula (4))which the complex conjugate generating circuit 15 outputs to the complexnumber signal 33, using C2(N−k) (Formula (6)) which the filtercoefficient generating circuit 41 outputs to the complex number signal46. Specifically, about each frequency number k of 0≦k≦N−1, the filtercircuit 22 calculates a complex number signal

X*′(N−k)=X*(N−k)×C2(N−k)  (8)

and outputs X*′(N−k) as a complex number signal 35.

Each of C1(k) and C2(k) can be written by being divided into a real partand an imaginary part as follows.

C1(k)=C1I(k)+jC1Q(k)  (9)

C2(k)=C2I(k)+jC2Q(k)  (10)

Next, the complex conjugate combining circuit 16 generates complexnumber signal X″(k) by combining X′(k) (Formula (7)) which the filtercircuit 21 outputs to the complex number signal 34 with X*′(N−k)(Formula (8)) which the filter circuit 22 outputs to the complex numbersignal 35. Specifically, about each of frequency number k of 0≦k≦N−1,the complex conjugate combining circuit 16 calculates

X″(k)=1/2×{X′(k)+X*′(N−k)}  (11)

and outputs it as a complex number signal 36.

Next, about each of frequency number k of 0≦k≦N−1, the IFFT circuit 14generates complex number signal x″(n) of the time domain for X″(k)(Formula (11)) which the complex conjugate combining circuit 16 outputsto the complex number signal 36 by IFFT, and outputs x″(n).

FIG. 2 is a block diagram showing detail of a structure of the complexconjugate generating circuit 15. The complex conjugate generatingcircuit 15: receives output of the FFT circuit 13 X(k) (=A(k)+jB(k):Formula (2)), and outputs X(k) just as it is; and also receives outputX(N−k) (=A(N−k)+jB(N−k): Formula (3)), and calculates

X*(N−k)=A(N−k)−jB(N−k)  (4)

and outputs X*(N−k).

Each of X(k) and X*(N−k) can be written by being divided into a realpart and an imaginary part as follows.

X(k)=XI(k)+jXQ(k)  (12)

X*(N−k)=X*I(N−k)+jX*Q(N−k)  (13)

FIG. 3 is a block diagram showing detail of a structure of the filtercircuit 21. The filter circuit 21 receives X(k) (=XI(k)+jXQ(k): Formula(12)) which the complex conjugate generating circuit 15 outputs to thecomplex signal line 32 and complex number coefficient C1(k)(=C1I(k)+jC1Q(k): Formula (9)), and calculates

$\begin{matrix}\begin{matrix}{{X^{\prime}(k)} = {{{XI}^{\prime}(k)} + {j\; {{XQ}^{\prime}(k)}}}} \\{= {{X(k)} \times C\; 1(k)}}\end{matrix} & (14)\end{matrix}$

and outputs X′(k).

Here, XI′(k) and XQ′(k) are the real part and the imaginary part ofX′(k), respectively, and are given by the following equation.

XI′(k)=XI(k)×C1I(k)−XQ(k)×C1Q(k)  (15)

XQ′(k)=XI(k)×C1Q(k)+XQ(k)×C1I(k)  (16)

FIG. 4 is a block diagram showing detail of a structure of the filtercircuit 22. The filter circuit 22 receives X*(N−k) (=X*I(N−k)+jX*Q(N−k):Formula (13)) which the complex conjugate generating circuit 15 outputsto a complex signal line 33 and complex number coefficient C2(k)(=C2I(k)+jC2Q(k): Formula (10)), calculates

$\begin{matrix}\begin{matrix}{{X^{*\prime}\left( {N - k} \right)} = {{X^{*}{I^{\prime}\left( {N - k} \right)}} + {j\; X^{*}{Q^{\prime}\left( {N - k} \right)}}}} \\{= {{X^{*}\left( {N - k} \right)} \times C\; 2\left( {N - k} \right)}}\end{matrix} & (17)\end{matrix}$

and outputs X*′(N−k).

Here, X*I′(N−k) and X*Q′(N−k) are the real part and the imaginary partof X*′(N−k), and are given by the following equations, respectively.

X*I′(N−k)=X*I(N−k)×C2I(N−k)−X*Q(N−k)×C2Q(N−k)  (18)

X*Q′(N−k)=X*I(N−k)×C2Q(N−k)+X*Q(N−k)×C2I(N−k)  (19)

FIG. 5 is a block diagram showing detail of a structure of the complexconjugate combining circuit 16. About each of frequency number k of0≦k≦N−1, the complex conjugate combining circuit 16 receives: X′(k)(=XI′(k)+jXQ′(k): Formula (14)) which the filter circuit 21 outputs tothe complex number signal 32; and X*′(N−k) (=X*I′(N−k)+jX*Q′(N−k):Formula (17)) which the filter circuit 22 outputs to the complex numbersignal 33, calculates

$\begin{matrix}\begin{matrix}{{X^{''}(k)} = {{{XI}^{''}(k)} + {j\; {{XQ}^{''}(k)}}}} \\{= {{1/2}\; \left\{ {{X^{\prime}(k)} + {X^{*\prime}\left( {N - k} \right)}} \right\}}}\end{matrix} & (20)\end{matrix}$

and outputs X″(k).

Here, XI″(k) and XQ″(k) are the real part and the imaginary part ofX″(k), respectively, and are given by the following equations.

XI″(k)=1/2{XI′(k)+X*I′(N−k)}  (21)

XQ″(k)=1/2{XQ′(k)+X*Q′(N−k)}  (22)

Here, XI′(k), XQ′(k), X*I′(N−k) and X*Q′(N−k) are respectively given bythe Formulas (15), (16), (18) and (19).

The filter coefficient generating circuit 41 generates the complexnumber coefficients C1(k) and C2(k) used in the filter circuits 21 and22. FIG. 6 is a block diagram showing detail of a structure of thefilter coefficient generating circuit 41. About each of frequency numberk of 0≦k≦N−1, the filter coefficient generating circuit 41 calculatesV(k)+W(k) and V(k)−W(k) from complex number coefficients V(k) and W(k)inputted from a higher rank circuit (not shown).

Here, they are as follows.

V(k)+W(k)=VI(k)+WI(k)+jVQ(k)+jWQ(k)  (23)

V(k)−W(k)=VI(k)−WI(k)+jVQ(k)−jWQ(k)  (24)

Here, VI(k) and VQ(k) are the real part and the imaginary part of V(k),respectively, and WI(k) and WQ(k) are the real part and the imaginarypart of W(k), respectively.

Also, H(k) can be written as follows in a manner being divided into thereal part and the imaginary part.

H(k)=HI(k)+jHQ(k)  (25)

Next, the filter coefficient generating circuit 41 calculates thecomplex number coefficients C1(k) and C2(k) defined by the followingFormulas and outputs C1(k) and C2(k).

$\begin{matrix}\begin{matrix}{{C\; 1(k)} = {{C\; 1\; {I(k)}} + {j\; C\; 1\; {Q(k)}}}} \\{= {\left\{ {{V(k)} + {W(k)}} \right\} \times {H(k)}}}\end{matrix} & (26) \\\begin{matrix}{{C\; 2(k)} = {{C\; 2\; {I(k)}} + {j\; C\; 2\; {Q(k)}}}} \\{= {\left\{ {{V(k)} - {W(k)}} \right\} \times {H(k)}}}\end{matrix} & (27)\end{matrix}$

Where, C1I(k) and C1Q(k) are the real part and the imaginary part ofC1(k), respectively, and C2I(k) and C2Q(k) are the real part and theimaginary part of C2(k), respectively.

When substituting Formula (23) and (25) into Formula (26), we get thefollowing formula.

C1(k)={VI(k)+WI(k)+jVQ(k)+jWQ(k)}×{HI(k)+jHQ(k)}  (28)

Accordingly, we obtain the following.

C1I(k)={VI(k)+WI(k)}×HI(k)−{VQ(k)+WQ(k)}×HQ(k)  (29)

C1Q(k)={VQ(k)+WQ(k)}×HI(k)+{VI(k)+WI(k)}×HQ(k)  (30)

Similarly, when Formula (24) and (25) are substituted into Formula (27),we get the following formula.

$\begin{matrix}\begin{matrix}{{C\; 2(k)} = {{C\; 2\; {I(k)}} + {j\; C\; 2\; {Q(k)}}}} \\{= {\left\{ {{V(k)} - {W(k)}} \right\} \times {H(k)}}} \\{= {\left\{ {{{VI}(k)} - {{WI}(k)} + {j\; {{VQ}(k)}} - {j\; {{WQ}(k)}}} \right\} \times \left\{ {{{HI}(k)} + {j\; {{HQ}(k)}}} \right\}}}\end{matrix} & (31)\end{matrix}$

Accordingly, we get the following.

C2I(k)={VI(k)−WI(k)}×HI(k)−{VQ(k)−WQ(k)}×HQ(k)  (32)

C2Q(k)={VQ(k)−WQ(k)}×HI(k)+{VI(k)−WI(k)}×HQ(k)  (33)

As above, the digital filter circuit 10 performs FFT conversion of aninput signal of the time domain, and generates a complex number signalof the frequency domain. Then, the digital filter circuit 10 performsfiltering processing to each of the real part and the imaginary part ofthe complex number signal of the frequency domain independently usingtwo kinds of coefficients generated from V(k), W(k) and H(k), andconverts the result of the processing into a signal of the time domainby IFFT. Thus, in the digital filter circuit 10, each of FFT and IFFT iscarried out only once to an input signal of the time domain.

Two kinds of coefficients used for filtering processing enable tominimize the number of times of FFT and IFFT. The physical meaning ofV(k), W(k) and H(k) and a principle by which filtering processing in thefrequency domain that is equal to desired filtering processing in thetime domain becomes possible by filtering processing using coefficientsC1(k) and C2 (k) generated from V(k), W(k) and H(k) will be describedbelow.

In this exemplary embodiment, from a complex number signal of thefrequency domain

X(k)=R(k)+jS(k)  (34)

which has been generated by performing complex FFT to inputted complexnumber signal x(n) (=r(n)+js(n): Formula (1)) of the time domain, thecomplex conjugate generating circuit 15 generates X*(N−k).

Here, R(k) is a complex number signal of the frequency domain made byconverting real part signal r(n) of a real number in the time domainusing real number FFT, and S(k) is a complex number signal of thefrequency domain made by converting imaginary part signal s(n) of a realnumber in the time domain using real number FFT. At that time, thefollowing equation holds from symmetry of complex conjugate.

X*(N−k)=R(k)−jS(k)  (35)

Here, X*(N−k) is the complex conjugate of X(N−k).

From Formulas (14), (34) and (26), we obtain the following.

$\begin{matrix}\begin{matrix}{{X^{\prime}(k)} = {{X(k)} \times C\; 1(k)}} \\{= {\left\{ {{R(k)} + {j\; {S(k)}}} \right\} \times \left\{ {{V(k)} + {W(k)}} \right\} \times {H(k)}}} \\{= {{{R(k)}{V(k)}{H(k)}} + {{R(k)}{W(k)}{H(k)}} + {j\; {S(k)}{V(k)}{H(k)}} +}} \\{{j\; {S(k)}{W(k)}{H(k)}}}\end{matrix} & (36)\end{matrix}$

Also, from Formulas (17), (35) and (27), we get the following.

$\begin{matrix}\begin{matrix}{{X^{*\prime}\left( {N - k} \right)} = {{X^{*}\left( {N - k} \right)} \times C\; 2\left( {N - k} \right)}} \\{= {\left\{ {{R(k)} - {j\; {S(k)}}} \right\} \times \left\{ {{V(k)} - {W(k)}} \right\} \times {H(k)}}} \\{= {{{R(k)}{V(k)}{H(k)}} - {{R(k)}{W(k)}{H(k)}} - {j\; {S(k)}{V(k)}{H(k)}} +}} \\{{j\; {S(k)}{W(k)}{H(k)}}}\end{matrix} & (37)\end{matrix}$

When Formulas (36) and (37) are substituted into Formula (20), we get

$\begin{matrix}\begin{matrix}{{X^{''}(k)} = {1\text{/}2 \times \left\{ {{X^{\prime}(k)} + {X^{*\prime}\left( {N - k} \right)}} \right\}}} \\{= {1\text{/}2 \times \left\{ {{2 \times {R(k)}{V(k)}{H(k)}} + {2 \times j\; {S(k)}{W(k)}{H(k)}}} \right\}}} \\{= {{{R(k)}{V(k)}{H(k)}} + {j\; {S(k)}{W(k)}{H(k)}}}} \\{= {\left\{ {{{R(k)}{V(k)}} + {j\; {S(k)}{W(k)}}} \right\} \times {H(k)}}}\end{matrix} & (38)\end{matrix}$

Formula (38) represents signal X″(k) that is a signal before IFFT usingfilter coefficients V(k), W(k) and H(k), and R(k) and S(k) in signalX(k) after FFT. R(k) is a complex number signal of the frequency domainmade by converting real part signal r(n) of a real number in the timedomain by real number FFT. S(k) is a complex number signal of thefrequency domain made by converting imaginary part signal s(n) of a realnumber in the time domain by real number FFT. In other words, Formula(38) represents the contents of filtering processing performed to signalX(k) after FFT. From Formula (38), it is found that the digital filtercircuit 10 performs processing equal to the following three pieces offiltering processing to complex number signal X(k) (=R(k)+jS(k): Formula(34)) of the frequency domain which has been generated by convertingcomplex number signal x(n)=r(n)+js(n) by real number FFT.

1) Filtering Processing for R(k) by Coefficient V(k)

First, the digital filter circuit 10 performs filtering processing byfilter coefficient V(k) to a complex number signal R(k) of the frequencydomain which has been made by converting real part signal r(n) in thetime domain by real number FFT. Accordingly, assigned to V(k) is acomplex number filter coefficient of the frequency domain correspondingto a real number filter coefficient when performing filtering processingby real number operation in the time domain to real part signal r(n).

2) Filtering Processing by Coefficient W(k) to S(k)

Similarly, the digital filter circuit 10 performs filtering processingby filter coefficient W(k) to a complex number signal S(k) of thefrequency domain which has been made by converting imaginary part signals(n) in the time domain by real number FFT. Accordingly, assigned to W(k) is a complex number filter coefficient of the frequency domaincorresponding to a real number filter coefficient when performingfiltering processing by real number operation in the time domain toimaginary part signal s(n).

3) Filtering Processing by Coefficient H(k) to Results of FilteringProcessing 1) and 2)

Next, the digital filter circuit 10 performs filtering processing byfilter coefficient H(k) to complex number signal R(k)V(k)+jS(k)W(k)which includes R(k)V(k) and S(k)W(k) after the above-mentioned twofiltering processing processed independently, respectively.

R(k)V(k)+jS(k)W(k) is a complex number signal of the frequency domaincorresponding to a signal of the time domain including two signals whichare signals made by performing filtering processing to each of real partsignal r(n) and imaginary part signal s(n) in the time domainindependently. A signal made by performing filtering processing to eachof real part signal r(n) and imaginary part signal s(n) independentlycorresponds to r′(n), s′(n) in FIGS. 9 and 10. Also, a signal of thetime domain including r′(n) and s′(n) corresponds to x′(n) of FIGS. 9and 10. Thus, R(k)V(k)+jS(k)W(k) is a signal of the frequency domaincorresponding to a signal of the time domain made by performingfiltering processing to each of the real part and the imaginary partindependently in the time domain.

Accordingly, in order to perform to signal R(k)V(k)+jS(k)W(k) of thefrequency domain processing corresponding to filtering processingperformed to a complex number signal in the time domain by complexnumber operation, the following coefficient should be used. That is, acomplex number filter coefficient in the frequency domain thatcorresponds to a complex number filter coefficient when performingfiltering processing by complex number operation in the time domain tocomplex number signal x(n) should be assigned to H(k).

As described above, three kinds of coefficient are set from outside inthis exemplary embodiment. That is, there are set: filter coefficientV(k) and W(k) of the frequency domain corresponding to filtercoefficients in the time domain for each of the real part and theimaginary part of complex number signal x(n); and coefficient H(k) ofthe frequency domain corresponding to a filter coefficient in the timedomain for x(n). By performing filtering processing using twocoefficients obtained from the above three coefficients, FFT before thefiltering processing and IFFT after the filtering processing can be madeto be only once, respectively.

By the way, FFT and IFFT in the digital filter circuit 10 are usualconversions respectively, and no processing unique to the presentinvention is performed. Therefore, FFT and IFFT may be processed by acircuit outside the digital filter circuit 10. That is, a digital filtercircuit may input a signal from an external Fourier conversion circuit,and perform only filtering processing, and output a processing result toan external inverse Fourier transform circuit. Accordingly, a blockdiagram of the digital filter circuit 110 having only an indispensablestructure of a filter circuit of this exemplary embodiment will be asshown in FIG. 7. A block diagram of FIG. 7 is a diagram made by removingthe FFT circuit 13 and the IFFT circuit 14 from the structure of FIG. 1.The digital filter circuit 110 includes the complex conjugate generatingcircuit 15, the complex conjugate combining circuit 16, the filtercircuit 21, the filter circuit 22 and the filter coefficient generatingcircuit 41. Because the function of each of these blocks is the same asthat of the digital filter circuit 10, description will be omitted.

When processing of FFT and IFFT is performed outside, circuits neededfor performing FFT and IFFT are only one respectively, and a pluralityof circuits, for such as a real part and an imaginary part, do not needto be used.

Effect of the First Exemplary Embodiment

As described above, according to this exemplary embodiment, filteringprocessing using two kinds of filter coefficient of frequency domaincorresponding to filter coefficients of the time domain for each of thereal part and the imaginary part of a complex number signal and acoefficient of the frequency domain corresponding to a filtercoefficient of the time domain for a complex signal is performed. Thatis, filtering processing in the frequency domain corresponding to:independent filtering processing by real number operation for each ofthe real part and the imaginary part of a complex number signal in thetime domain; and filtering processing by complex number operation for acomplex number signal in the time domain is performed. Accordingly,desired filtering processing can be realized using only one FFT circuitwhich performs FFT before the filtering processing and one IFFT circuitwhich performs IFFT after the filtering processing. As a result, thisexemplary embodiment has an effect that reduction in a circuit size andpower consumption for performing filtering processing can be achieved.

Second Exemplary Embodiment

In the first exemplary embodiment, it is assumed that all of each pieceof processing of FFT, IFFT, generation and combining of a conjugatecomplex number, calculation of a filter coefficient and filteringprocessing are processed by components such as individual circuits. Eachpiece of processing of the present invention may be carried out, not bythe form like the first exemplary embodiment, but by software that usesa computer provided in predetermined equipment such as a DSP (DigitalSignal Processor).

In the second exemplary embodiment, an example when performing filteringprocessing by a computer program is described. A computer program isread by a DSP (not shown) and executed. Meanwhile, in this exemplaryembodiment, a structure of an exemplary embodiment is not shown inparticular because hardware besides a computer which performs programprocessing is not used.

FIGS. 8A and 8B are flow charts showing an example of a processingprocedure of a filtering processing program of the second exemplaryembodiment of the present invention. A signal name such as X(k) and aninformation name such as V(k) used in the following description are thesame as those used in the first exemplary embodiment.

In the processing of FIG. 8A, at first, a DSP obtains C1(k) and C2(k)from V(k), W(k) and H(k) (Step S0). Meanwhile, the processing of Step 0should simply be carried out before filtering processing (Steps S3 andS4) mentioned later, and does not need to be carried out firstnecessarily.

Next, the DSP performs Fourier transform to input signal X(n) (Step S1),and generates X(k) and X(N−k).

Furthermore, the DSP obtains conjugate complex number X*(N−k) of X(N−k)(Step S2).

Then, the DSP performs filtering processing to X(k) using C1(k), andgenerates X′(k) (Step S3). The DSP performs filtering processing toX*(N−k) using C2(k), and generates X*′(N−k) (Step S4). Order ofprocessing of Step S3 and Step S4 may be reversed to the abovedescription.

Next, the DSP combines X′(k) and X*′(N−k), and obtains X″(k) (Step S5).

Finally, the DSP performs inverse Fourier transform to X″(k), andobtains x″(n) (Step S6).

As above, the contents of filtering processing of the second exemplaryembodiment are the same as those of the first exemplary embodiment.Accordingly, there is the same effect as the first exemplary embodimentin the filtering processing of the second exemplary embodiment.

Meanwhile, calculation of filter coefficients C1(k) and C2(k) may beperformed by a different program in advance. In that case, a flow chartshowing operations will be like FIG. 8B because processing of Step 0becomes unnecessary. In addition, individual processing such as FFT andIFFT may be processed by other processors.

The above-mentioned filtering processing program may be stored in anon-temporary medium such as: a semiconductor memory device, such as ROM(Read Only Memory), RAM (Random Access Memory) and a flash memory; anoptical disk; a magnetic disk; and a magneto-laser disk.

The first exemplary embodiment and the second exemplary embodiment maybe combined. That is, part of processing may be processed by hardware,and the other processing may be processed by software. For example, FFTand IFFT may be processed using the FFT circuit 13 and the IFFT circuit14, respectively, and the other processing be carried out by software.An assignment of processing by hardware and processing by software canbe determined freely.

Although the present invention has been described with reference to anexemplary embodiment above, the present invention is not limited to theabove-mentioned exemplary embodiments. Various modifications which aperson skilled in the art can understand can be made in the compositionand details of the present invention within the scope of the presentinvention.

This application claims priority based on Japanese application JapanesePatent Application No. 2012-034002, filed on Feb. 20, 2012, thedisclosure of which is incorporated herein in its entirety.

REFERENCE SIGNS LIST

-   -   10 Digital filter circuit    -   13 FFT circuit    -   14 IFFT circuit    -   15 Complex conjugate generating circuit    -   16 Complex conjugate combining circuit    -   21 Filter circuit    -   22 Filter circuit    -   31-36 Complex number signal    -   41 Filter coefficient generating circuit    -   45 and 46 Complex number signal    -   100 Digital filter circuit    -   101-103 FIR filter    -   111-113 Frequency domain filter circuit

What is claimed is:
 1. A digital filter circuit, comprising: a complexconjugate generation unit that generates a second complex number signalincluding respective conjugate complex numbers of all complex numbersincluded in a first complex number signal of a frequency domaingenerated by converting a complex number signal of a time domain byFourier transform; a filter coefficient generation unit that generates afirst and a second frequency domain filter coefficient of a complexnumber from a first, a second and a third input filter coefficient of acomplex number having been inputted; a first filtering unit thatperforms filtering processing to the first complex number signal by thefirst frequency domain filter coefficient, and outputting a thirdcomplex number signal; a second filtering unit that performs filteringprocessing to the second complex number signal by the second frequencydomain filter coefficient, and outputting a fourth complex numbersignal; and a complex conjugate combining unit that combines the thirdcomplex number signal and the fourth complex number signal, andgenerating a fifth complex number signal.
 2. The digital filter circuitaccording to claim 1, further comprising: a Fourier transform unit thatconverts the complex number input signal of the time domain having beeninputted into the first complex number signal by the Fourier transform;and an inverse Fourier transform unit that converts the fifth complexnumber signal into a signal of the time domain by inverse Fouriertransform.
 3. The digital filter circuit according to claim 1, wherein,when assuming that the number of conversion samples of the Fouriertransform is N (N is an integer of N>0), the complex conjugategeneration unit generates a conjugate complex number of a complex numbersignal of frequency number (N−k) included in the first complex numbersignal as the second complex number signal.
 4. The digital filtercircuit according to claim 3, wherein the complex conjugate combiningunit means generates the fifth complex number signal by performing, foreach of frequency number k in a range of 0≦k≦N−1, complex addition offirst complex data of frequency number k included in the third complexnumber signal and a second complex data of frequency number (N−k)included in the fourth complex number signal.
 5. The digital filtercircuit according to claim 1, wherein the filter coefficient generationunit: generates the first frequency domain filter coefficient by, afterperforming complex addition of the second input filter coefficient tothe first input filter coefficient, further performing complexmultiplication by the third input filter coefficient; and generates thesecond frequency domain filter coefficient by, after performing complexsubtraction of the second input filter coefficient from the first inputfilter coefficient, further performing complex multiplication by thethird input filter coefficient.
 6. The digital filter circuit accordingto claim 1, wherein the first frequency domain filter coefficient is acomplex number filter coefficient of the frequency domain correspondingto a filter coefficient for a real part of the complex input signal in atime domain filtering processing, the time domain filtering processingbeing filtering processing of the time domain for the complex inputsignal, wherein the second frequency domain filter coefficient is acomplex number filter coefficient of the frequency domain correspondingto a filter coefficient for an imaginary part of the complex inputsignal in the time domain filtering processing, and wherein the thirdfrequency domain filter coefficient is a complex number filtercoefficient of the frequency domain corresponding to a filtercoefficient for the complex number input signal in the time domainfiltering processing.
 7. A digital filter processing method, comprising:generating a second complex number signal including respective conjugatecomplex numbers of all complex numbers included in a first complexnumber signal of a frequency domain generated by converting a complexnumber signal of a time domain by Fourier transform; generating a firstand a second frequency domain filter coefficient of a complex numberfrom a first, a second and a third input filter coefficient of a complexnumber having been inputted; performing filtering processing to thefirst complex number signal by the first frequency domain filtercoefficient, and outputting a third complex number signal; performingfiltering processing to the second complex number signal by the secondfrequency domain filter coefficient, and outputting a fourth complexnumber signal; and combining the third complex number signal and thefourth complex number signal, and generating a fifth complex numbersignal.
 8. A non-transitory storage medium storing a digital filterprocessing program for making a computer provided in an arithmeticdevice function as: a complex conjugate generation unit that generates asecond complex number signal including respective conjugate complexnumbers of all complex numbers included in a first complex number signalof a frequency domain generated by converting a complex number signal ofa time domain by Fourier transform; a filter coefficient generation unitthat generates a first and a second frequency domain filter coefficientof a complex number from a first, a second and a third input filtercoefficient of a complex number having been inputted; a first filteringprocessing unit that performs filtering processing to the first complexnumber signal by the first frequency domain filter coefficient, andoutputting a third complex number signal; a second filtering processingunit that performs filtering processing to the second complex numbersignal by the second frequency domain filter coefficient, and outputtinga fourth complex number signal; and a complex conjugate combining unitthat combines the third complex number signal and the fourth complexnumber signal, and generating a fifth complex number signal.